reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th61:
  for H being strict Subgroup of G holds H |^ 1_G = H
proof
  let H be strict Subgroup of G;
  the carrier of H |^ 1_G = carr H |^ 1_G by Def6
    .= the carrier of H by Th52;
  hence thesis by GROUP_2:59;
end;
